Foundations of Astronomy (MindTap Course List)
14th Edition
ISBN: 9781337399920
Author: Michael A. Seeds, Dana Backman
Publisher: Cengage Learning
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Chapter 12, Problem 1SOP
To determine
The lifespan on the main-sequence of an
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White Dwarf Size II. The white dwarf, Sirius B, contains 0.98 solar mass, and its density is about 2 x 106 g/cm?. Find the radius of the white dwarf in km to three significant digits. (Hint: Density = mass/volume, and the volume of a
4
sphere is Tr.)
3
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Compare your answer with the radii of the planets listed in the Table A-10. Which planet is this white dwarf is closely equal to in size?
I Table A-10 I Properties of the Planets
ORBITAL PROPERTIES
Semimajor Axis (a)
Orbital Period (P)
Average Orbital
Velocity (km/s)
Orbital
Inclination
Planet
(AU)
(106 km)
(v)
(days)
Eccentricity
to Ecliptic
Mercury
0.387
57.9
0.241
88.0
47.9
0.206
7.0°
Venus
0.723
108
0.615
224.7
35.0
0.007
3.4°
Earth
1.00
150
1.00
365.3
29.8
0.017
Mars
1.52
228
1.88
687.0
24.1
0.093
1.8°
Jupiter
5.20
779
11.9
4332
13.1
0.049
1.30
Saturn
9.58
1433
29.5
10,759
9.7
0.056
2.5°
30,799
60,190
Uranus
19.23
2877
84.3
6.8
0.044
0.8°
Neptune
* By definition.
30.10
4503
164.8
5.4
0.011
1.8°
PHYSICAL PROPERTIES (Earth = e)…
Using solar units, we find that a star has 4 times the luminosity of the Sun, a mass 1.25 times the mass of the Sun, and a surface temperature of 4090 K (take the Sun's surface temperature to be 5784 K for the sake of this problem). This means the star has a radius of.................... solar radii and is a .................... star (use the classification).
12: A star with spectral type A0 has a surface temperature of 9600 K and a radius of 2.2 RSun. How many times more luminous is this star than the Sun? (if it is less luminous enter a number less than one)
Answer: 36.854
13:This star has a mass of 3.3 MSun. what is the main sequence lifetime of this star? You may assume that the lifetime of the sun is 1010 yr.
Please answer question 13 thank you.
Chapter 12 Solutions
Foundations of Astronomy (MindTap Course List)
Ch. 12 - Prob. 1RQCh. 12 - Prob. 2RQCh. 12 - Prob. 3RQCh. 12 - Prob. 4RQCh. 12 - Prob. 5RQCh. 12 - Describe the law of hydrostatic equilibrium.Ch. 12 - Prob. 7RQCh. 12 - Prob. 8RQCh. 12 - Prob. 9RQCh. 12 - Prob. 10RQ
Ch. 12 - Prob. 11RQCh. 12 - Prob. 12RQCh. 12 - Prob. 13RQCh. 12 - Prob. 14RQCh. 12 - Prob. 15RQCh. 12 - Prob. 16RQCh. 12 - Prob. 17RQCh. 12 - Prob. 18RQCh. 12 - Prob. 19RQCh. 12 - What gives the triple-alpha process its name? Why...Ch. 12 - Prob. 21RQCh. 12 - Prob. 22RQCh. 12 - Prob. 23RQCh. 12 - Prob. 24RQCh. 12 - Prob. 25RQCh. 12 - Prob. 26RQCh. 12 - Prob. 27RQCh. 12 - Prob. 28RQCh. 12 - Prob. 29RQCh. 12 - Prob. 30RQCh. 12 - Prob. 31RQCh. 12 - How Do We Know? How can mathematical models allow...Ch. 12 - Prob. 1PCh. 12 - Prob. 2PCh. 12 - Prob. 3PCh. 12 - Prob. 4PCh. 12 - Prob. 5PCh. 12 - Prob. 6PCh. 12 - Prob. 7PCh. 12 - Prob. 8PCh. 12 - Prob. 9PCh. 12 - Prob. 10PCh. 12 - Prob. 11PCh. 12 - Prob. 12PCh. 12 - Prob. 13PCh. 12 - Prob. 14PCh. 12 - Prob. 15PCh. 12 - Prob. 16PCh. 12 - Prob. 1SOPCh. 12 - Prob. 2SOPCh. 12 - Prob. 1LTLCh. 12 - Prob. 2LTLCh. 12 - Prob. 3LTLCh. 12 - Prob. 4LTLCh. 12 - Prob. 5LTL
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- This star has a mass of 3.3 MSun. What is the main sequence lifetime of this star? You may assume that the lifetime of the sun is 1010 yr.arrow_forwardA main sequence star of mass 25 M⊙has a luminosity of approximately 80,000 L⊙. a. At what rate DOES MASS VANISH as H is fused to He in the star’s core? Note: When we say “mass vanish '' what we really mean is “gets converted into energy and leaves the star as light”. Note: approximate answer: 3.55 E14 kg/s b. At what rate is H converted into He? To do this you need to take into account that for every kg of hydrogen burned, only 0.7% gets converted into energy while the rest turns into helium. Approximate answer = 5E16 kg/s c. Assuming that only the 10% of the star’s mass in the central regions will get hot enough for fusion, calculate the main sequence lifetime of the star. Put your answer in years, and compare it to the lifetime of the Sun. It should be much, much shorter. Approximate answer: 30 million years.arrow_forwardThe mass-luminosity relation describes the mathematical relationship between luminosity and mass for main sequence stars. It describes how a star with a mass of 4 M⊙ would have a luminosity of ______ L⊙. If a star has a radius 1/2 that of the Sun and a temperature 4 that of the Sun, how many times higher is the star's luminosity than that of the Sun? (If it is smaller by a factor of 8, you would write 0.125 because 1/8=0.125) If a star has a radius 2 times larger than the Sun's and a luminosity 1/4th that of the Sun, how many times higher is the star's temperature than that of the Sun? (If it is smaller by a factor of 8, you would write 0.125 because 1/8=0.125) If a star has a surface temperature 2 times lower than the Sun's and a luminosity the same as the Sun, how many times larger is the star than the Sun? (If it is smaller by a factor of 8, you would write 0.125 because 1/8=0.125)arrow_forward
- Observations show that stellar luminosity, L, and mass, M, are related by L x M3.5 for main sequence stars. Obtain an expression that relates the main sequence life time and the mass of a star. You should assume that the luminosity is constant throughout a star's main sequence life time, and that the amount of mass converted into energy by a star while it is on the main sequence is given by AM main sequence life time of a 20 Solar mass star given that the Sun is expected to spend 1010 years on the main sequence. Comment on the significance of your answer. fM, where f is a constant. Estimate thearrow_forwardStar A and Star B are both on the main sequence. Star A is 74 times more luminous than Star B. What is the ratio of their main-sequence lifetimes? Hint: Refer to the stellar life expectancies equation,arrow_forwardLet's calculate how much mass will be lost by the Sun during the course of its main-sequence lifetime. While it is on the main sequence, a star converts about 10% of the hydrogen initially present into helium (remember that it is only the core of the star that is hot enough for fusion). During nuclear fusion, the Sun converts about 0.7% of the core hydrogen mass into energy. The total mass of the Sun is 2 × 1030 kg. How many kilograms of mass will be converted to energy during the main sequence stage of the Sun's life? What is the ratio of this lost mass to the Earth's mass (6 × 1024 kg)? In other words, how many Earths of mass will be turned into energy?arrow_forward
- A star with spectral type A0 has a surface temperature of 9600 K and a radius of 2.2 RSun. How many times more luminous is this star than the Sun? (if it is less luminous enter a number less than one) This star has a mass of 3.3 MSun. Using the simple approximation that we made in class, what is the main sequence lifetime of this star? You may assume that the lifetime of the sun is 1010 yr. Compare this to the lifetime of a A0 star listed in Table 22.1 (computed using a more sophisticated approach). Is the value you calculated in the previous problem longer or shorter than what is reported in the table? (L for longer, S for shorter) (You only get one try at this problem.)arrow_forwardSuppose a star has a luminosity of 7.0x1026 watts and an apparent brightness of 4.0x10-12 watt/m?. How far away is it? Give your answer in both kilometers and light-years.arrow_forwardConsider two stars on the main sequence, A and B. Star A has a mass of Мо Star B has a mass of 0.2 Мо By what factor is the luminosity of star A greater than the luminosity of star В? [Hint: use the proportionality relations for mass, luminosity, or lifetime for stars on the main sequence.]arrow_forward
- Let us imagine that the spectrum of a star is collected and we find the absorption line of Hydrogen-Alpha (the deepest absorption line of hydrogen in the visible part of the electromagnetic spectrum) to be observed at 656.5 nm instead of 656.3 nm as measured in a lab here on Earth. What is the velocity of this star in m/s? (Hint: speed of light is 3*10^8 m/s; leave the units off of your answer)arrow_forwardAssuming that at the end of the He burning phase of the stellar core (r < R_core) has no H or He or other metals and is composed completely of Carbon, X=Y=0, X_c = 1 ; The envelope above the core has a normal stellar composition ( r > R_core). Calculate the length of time in years that a 1M_sol and 10M_sol star will live on the horizontal branch or the time between the start and end of the He burning phase. Assume that the normal relationship between mass and luminosity holds for horizontal branch stars. Please be as detailed as possiblearrow_forwardHow does one go about these questions?arrow_forward
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